Efficient evaluation of Arrhenius rates for quantum computing applications in reactive flow problems using Carleman linearization
Takaki Akiba, Youhi Morii, Minhyeok Lee, Kaoru Maruta, Yuji Suzuki · Proceedings of the Combustion Institute · 2025
This research introduces a novel approach toward integrating quantum computing into reactive flow analysis in combustion science, addressing the challenges posed by the nonlinear behavior of Arrhenius reaction rates. Combustion systems are described by nonlinear equations. Quantum computers, however, work based on linear algebra and are good at solving linear systems, necessitating a method to bridge this disparity. The study utilizes Carleman linearization, a technique that transforms nonlinear equations into linear ones, making them suitable for quantum algorithms. To address the exponential temperature dependence of Arrhenius rate constants, Taylor series expansions are employed. The method is validated through numerical simulations of ignition in H 2 /air and CH 4 /air mixtures. By examining the impact of truncation order in Carleman linearization and fitting order in the Taylor expansion, the study balances computational accuracy and cost. Results reveal that higher-order approximations improve accuracy but can introduce numerical stiffness, particularly in systems with high activation energies, such as CH 4 /air in this study. The findings highlight the trade-offs between computational feasibility and solution precision, emphasizing the importance of optimizing fitting and truncation parameters. This work establishes a critical foundation for applying quantum computing to combustion research.